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0 Session 8B: Well-Being Over Time II Time: Friday, August 10, 2012 PM Paper Prepared for the 32nd General Conference of The International Association for Research in Income and Wealth Boston, USA, August 5-11, 2012 Inequality of Income and Consumption: Measuring the Trends in Inequality from 1985-2010 for the Same Individuals Jonathan Fisher, David S. Johnson and Timothy M. Smeeding For additional information please contact: Name: David S. Johnson Affiliation: U.S. Census Bureau Email Address: , [email protected] This paper is posted on the following website: http://www.iariw.org

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Page 1: Boston, USA, August 5-11, 2012 · Boston, USA, August 5-11, 2012 Inequality of Income and Consumption: Measuring the Trends in Inequality from 1985-2010 for the Same Individuals Jonathan

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Session 8B: Well-Being Over Time II

Time: Friday, August 10, 2012 PM

Paper Prepared for the 32nd General Conference of

The International Association for Research in Income and Wealth

Boston, USA, August 5-11, 2012

Inequality of Income and Consumption:

Measuring the Trends in Inequality from 1985-2010 for the Same Individuals

Jonathan Fisher, David S. Johnson and Timothy M. Smeeding

For additional information please contact:

Name: David S. Johnson

Affiliation: U.S. Census Bureau

Email Address: , [email protected]

This paper is posted on the following website: http://www.iariw.org

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Inequality of Income and Consumption:

Measuring the Trends in Inequality from 1985-2010 for the Same Individuals

by

Jonathan Fisher

U.S. Census Bureau

David S. Johnson*

U.S. Census Bureau

Timothy M. Smeeding

University of Wisconsin

Paper Prepared for the 32nd General Conference of

The International Association for Research in Income and Wealth

Session 8B: Well-Being Over Time II

_________________ * Research conducted while a Visiting Scholar at Russell Sage Foundation. Contact David S. Johnson at U.S.

Census Bureau, Room 7H174, Washington, DC, 20233, [email protected].

Timothy Smeeding recognizes the support of the Institute for Research on Poverty (IRP) at the University of

Wisconsin-Madison. The researchers would like to thank Laura Paszkiewicz and Geoffrey Paulin for help with

income imputation and tax estimation.

The views expressed in this research, including those related to statistical, methodological, technical, or operational

issues, are solely those of the authors and do not necessarily reflect the official positions or policies of the Census

Bureau, the IRP, or the views of other staff members. The authors accept responsibility for all errors. This paper is

released to inform interested parties of ongoing research and to encourage discussion of work in progress.

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“The year 2011 will be remembered as the year when the idea of income inequality migrated

from seminar rooms in colleges and think tanks to Zuccotti Park and main streets across

America.”

Senior Fellow Isabel Sawhill, The Brookings Institution, April 2012

“What is making people sit up now is recent evidence that the richest 1 percent of American

families appears to have reaped most of the gains from the prosperity of the last decade and a

half.”

Columnist Sylvia Nasar, The New York Times, March 1992

I. Introduction: Income and Consumption

The 2012 Economic Report of the President stated: “The confluence of rising inequality

and low economic mobility over the past three decades poses a real threat to the United States as

a land of opportunity.” This view was also repeated in a speech by Council of Economics

Advisors Chairman, Alan Krueger (2012). President Obama suggested that inequality was

“…the defining issue of our time...” As suggested by Isabel Sawhill (2012), 2011 was the year

of inequality.

While there has been an increased interest in inequality, and especially the differences in

trends for the top 1 percent vs. the other 99 percent, this increase in inequality is not a new issue.

Twenty years ago, Sylvia Nasar (1992) highlighted similar differences in referring to a report by

the Congressional Budget Office (CBO) and Paul Krugman introduced the “staircase vs. picket

fence” analogy (see Krugman (1992)). He showed that the change in income gains between

1973 and 1993 followed a staircase pattern with income growth rates increasing with income

quintiles, a pattern that has been highlighted by many recent studies, including the latest CBO

(2011) report. He also showed that the income growth rates were similar for all quintiles from

1947-1973, creating a picket fence pattern across the quintiles.

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Recent research shows that income inequality has increased over the past three decades

(Burkhauser, et al. (2012), Smeeding and Thompson (2011), CBO (2011), Atkinson, Piketty and

Saez (2011)). And most research suggests that this increase is mainly due to the larger increase

in income at the very top of the distribution (see CBO (2011) and Saez (2012)). Researchers,

however, dispute the extent of the increase. The extent of the increase depends on the resource

measure used (income or consumption), the definition of the resource measure (e.g., market

income or after-tax income), and the population of interest.

This paper examines the distribution of income and consumption in the US using data

that obtains measures of both income and consumption from the same set of individuals and this

paper develops a set of inequality measures that show the increase in inequality during the past

25 years using the 1984-2010 Consumer Expenditure (CE) Survey.

The dispute over whether income or consumption should be preferred as a measure of

economic well-being is discussed in the National Academy of Sciences (NAS) report on poverty

measurement (Citro and Michael (1995), p. 36). The NAS report argues:

“Conceptually, an income definition is more appropriate to the view that what matters

is a family’s ability to attain a living standard above the poverty level by means of its

own resources…. In contrast to an income definition, an expenditure (or

consumption) definition is more appropriate to the view that what matters is

someone’s actual standard of living, regardless of how it is attained. In practice the

availability of high-quality data is often a prime determinant of whether an income-

or expenditure-based family resource definition is used.”

We agree with this statement and we would extend it to inequality measurement.1 In

cases where both measures are available, both income and consumption are important indicators

for the level of and trend in economic well-being. As argued by Attanasio, Battistin, and Padula

1 Borooah and McGregor (1992) suggest that consumption should be used as a measure of the standard of living and

that income should be used as a measure of the level of resources. Others may argue that net worth is an equally

important measure of well-being. For an attempt to capture the flow value of net worth and income but not

consumption, see Smeeding and Thompson (2011).

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(2010) “...the joint consideration of income and consumption can be particularly informative.”

Both resource measures provide useful information by themselves and in combination with one

another. When measures of inequality and economic well-being show the same levels and trends

using both income and consumption, then the conclusions on inequality are clear. When the

levels and/or trends are different, the conclusions are less clear, but useful information and an

avenue for future research can be provided.

We examine the trend in the distribution of these measures from 1985 to 2010. We show

that while the level of and changes in inequality differ for each measure, inequality increases for

all measures over this period and, as expected, consumption inequality is lower than income

inequality. Differing from other recent research, we find that the trends in income and

consumption inequality are similar between 1985 and 2006, and diverge during the first few

years of the Great Recession (between 2006 and 2010). For the entire 25 year period we find

that consumption inequality increases about two-thirds as much as income inequality. We show

that the quality of the CE survey data is sufficient to examine both income and consumption

inequality. Nevertheless, given the differences in the trends in inequality, using measures of

both income and consumption provides useful information. In addition, we present the level of

and trends in inequality of both the maximum and the minimum of income and consumption.

The maximum and minimum are useful to adjust for life-cycle effects of income and

consumption and for potential measurement error in income or consumption. The trends in the

maximum and minimum are also useful when consumption and income alone provide different

results concerning the measurement of economic well-being.

Our analysis differs from the most recent studies of consumption inequality (Heathcote,

et al. (2010), Perri and Steinberg (2012), Attanasio et al. (2012), and Meyer and Sullivan (2009))

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by not restricting the sample to specific demographic groups, by using a more complete measure

of consumption, and by using measures of income and consumption that are consistent with each

other, where both income and consumption are taken from the same households in a single

survey. Previous studies (e.g., Attanasio, et al. (2012) and Heathcote, et al. (2010)) restrict their

samples to the working age population and use only a subset of consumption, and Meyer and

Sullivan (2009) remove health care and education from consumption. Our study contributes to

the literature by providing a more complete measure of consumption without sample restrictions

that is better linked to disposable income, in order to more fully capture the levels and trends in

the distribution.

The paper is organized as follows. The second section of the paper evaluates the issues

associated with choosing a measure of economic well-being to assess the level of and trend in

inequality and examines the recent literature on inequality measurement. Section three presents

our methodology, our measures of income and consumption, and a description of the CE Survey

data. The fourth section presents the levels of and trends in inequality and the fifth section

discusses the implications for measurement error. Next we present our maximum and minimum

approach designed to bound inequality measures. The final section concludes this paper.

II. Recent Literature on Consumption and Income Inequality

Most inequality studies use annual income data (e.g., Burkhauser, et al. (2012), CBO

(2011), Atkinson, Piketty, and Saez (2011), Karoly (1993), Thompson and Smeeding (2012),

Smeeding and Thompson (2011), Gottschalk and Smeeding (1997)). There is agreement that

inequality increased using various measures of income, but the magnitude of the increase

depends on the income measure used and the unit of observation. For example, the Census

Bureau estimates that the inequality, using the Gini coefficient, of pre-tax cash income for

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households (adjusted for family size) increased 19 percent between 1979 and 2010. CBO (2012)

estimates an increase of 21.6 percent for market income inequality (between 1979 and 2009) and

a 19.0 percent increase in the inequality for after-tax-and-transfer income. Finally Saez (2012),

using the share of taxable income obtained by the top 1 percent, shows that the share of income

obtained by the top 1 percent doubled between 1979 and 2009.

A difficulty with using annual income to measure inequality is that if everyone goes

through a life-cycle current-income path in which income is low when young, higher in middle

age, and low again when old, then annual snapshots of income would suggest greater inequality

than that which actually exists in permanent income. It could be that all visible differences in the

level of and trend in inequality may be attributable to demographics alone.2 In addition, people

may experience many transitory changes in income that would cause the distribution of annual

income to indicate more inequality than actually exists. Gottschalk and Moffitt (2009) find that

about one-half of the increase in income inequality during the 1980s resulted from changes in

transitory income.3 Thus, annual income may be a poor proxy for permanent income.

Economists have suggested that consumption may be a more appropriate indicator of

permanent income (see Slesnick (1994), Cutler and Katz (1991), Johnson and Shipp (1997),

Johnson, Smeeding and Torrey (2005), and Krueger and Perri (2006)). Slesnick (2001), Cutler

and Katz (1991), and Danziger and Tausig (1979) were among the first to show different trends

in income and consumption inequality. The two former studies demonstrated that consumption

inequality was lower than income inequality, and that the increase in both income and

consumption inequality was similar during the 1980s. Krueger and Perri (2006) identify the

2 Deaton and Paxson (1994) discuss the importance of life-cycle effects in inequality measurement.

3 They show that while the increase in transitory variance explains about a quarter of the increase in inequality

between 1974-1990, during the 1990s the permanent variance falls, and hence, between 1974 and 2000, the increase

in transitory variance explains about 60% of the increase in inequality.

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divergent trends in income and consumption inequality during the 1990s. 4

Most recent research

shows that consumption inequality is less than income inequality, and its increase is less than the

increase in income inequality (see Krueger and Perri (2006), Heathcote, Perri and Violante

(2010), Blundell, Preston, and Pistaferri (2008), Petev, Pistaferri and Eksten, (2011), Meyer and

Sullivan (2009), Johnson and Shipp (1997)). A key similarity among these studies is that much

of the increase in consumption inequality occurred in the early 1980s. Heathcote, Perri and

Violante (2010) find that between 1980 and 2006, income inequality increases about twice as

much as consumption inequality. However, restricting the data to the change between 1985 and

2005 yields similar increases in inequality.

Three studies find similar increases in consumption and income inequality by adjusting

the CE Interview Survey data, which is used by most research on consumption inequality, or by

using an alternative data source. First, Attanasio, et al. (2006) use the CE Diary Survey (a

weekly record of expenditures) to calculate inequality, and find that consumption inequality rises

much more rapidly than that using the standard CE Interview Survey. Second, Aguiar and Bils

(2011) adjust the expenditure data in the CE Interview Survey for underreporting by using the

Engel curves estimated using the 1972-73 CE Interview Survey and obtain larger increases in

inequality, with consumption inequality increasing about the same rate as income inequality

between 1980 and 2007. Third, Attansio, et al. (2012) estimate consumption in the Panel Study

of Income Dynamics (PSID) using various methodologies and find that consumption and income

inequality rise by about the same percentage between 1980 and 2010.

In addition to finding similar increases in income and consumption inequality, these three

papers claim that the CE Interview Survey data are flawed. Attanasio, et al. (2012) claim that the

4 Research shows that this pattern holds across countries – permanent shocks translate into consumption changes,

while transitory shocks do not (see Brugiavin and Weber (2011)).

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CE Interview Survey suffers from “serious non-classical measurement error” and that the

increase in consumption inequality is under-estimated. Aguiar and Bils (2011) make a similar

claim and both papers attempt to adjust the data by changing the expenditure patterns between

low and high income households. Both suggest that the decline in the ratio between CE and the

Personal Consumption Expenditures (PCE) is the result of increased underreporting at the higher

end of the distribution. Bee, Meyer, and Sullivan (2012) conduct a validation study of the CE

Survey and state that “[t]he Interview Survey does quite well in terms of a high and roughly

constant share of expenditures relative to the national accounts for some of the largest

components of consumption.” Even if it was agreed that the consumption data were problematic,

to properly compare the adjusted consumption data to the income data, the income data would

also need to be adjusted (see Fixler and Johnson (2012)).

As with income, there is no agreed upon definition of consumption and no agreed upon

unit of observation. Johnson, Smeeding and Torrey (2005) and Meyer and Sullivan (2010) use

total consumption, including the service flows from vehicles and owned homes. Other studies

measure non-durable spending, but there is no consistent definition of non-durable spending. For

example, Heathcote, et al. (2006) include medical care while Attanasio, et al. (2012) excludes

medical care. Most, but not all, research limits the sample to urban households and to those that

are considered complete income reporters by the CE Survey.

III. Methodology and Data

Given the different definitions of income and consumption in the literature, it is important

to use a consistent theoretical framework to define these measures. It is also important to

account for potential measurement error in income and consumption, not just one or the other.

This section describes how we define income and consumption, how we deal with potential

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measurement error in both, and how we use the CE Survey data, but first we provide justification

for looking at both income and consumption.

Why income and consumption?

The Report by the Commission on the Measurement of Economic Performance and

Social Progress (or Stiglitz (2009) report) stated: “Income and its distribution are meaningful

ways to assess living standards. Another candidate is consumption and its distribution among

individuals. While correlated with income, consumption and its distribution are not necessarily

identical to income and several reasons account for this.” The report continues, “Empirical

research has repeatedly shown that the distribution of consumption can be quite different from

the distribution of income. Indeed, the most pertinent measures of the distribution of material

living standards are probably based on jointly considering the income, consumption, and wealth

position of households or individuals.”

Which measure is “best” depends mostly on how economic well-being is viewed and the

purpose for using the measure. Economic theory suggests that a household’s well-being (as

measured by the household’s utility) depends on the household’s characteristics and its

consumption levels. The life-cycle/permanent-income hypothesis (LCPIH) suggests that the

household’s well-being depends on the current-income stream that occurs over the household’s

lifetime. The LCPIH assumes households can smooth consumption through personal savings or

credit markets. As a consequence, households should change their consumption plans in

response to permanent shocks to income and they should only react to the annuitized value of

transitory shocks. At the other extreme, assuming that households have access to complete

markets in which they are able to completely insure against any shocks, then consumption should

not react to either permanent or transitory income shocks. If households have access to some

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insurance mechanism (formal or informal), they will be able to smooth out, at least in part,

income shocks. According to the LCPIH, a household smooths consumption over the

household’s lifetime so that even if income varies significantly over the life-cycle, consumption

is less variable than income from year to year. This suggests that consumption data should be

used as the preferred measure of permanent income and household well-being.

In a world of perfect information, with liquid assets and no borrowing constraints and

with accurate cross-sectional surveys that measure both income and consumption, the best

measure of permanent income would be consumption. Because foresight is imperfect, borrowing

constraints exist, and perfect surveys do not exist, both annual income and consumption are

needed to obtain an approximation of economic well-being. Neither measure alone captures the

economic well-being of all households.

As stated by the NAS report, “In practice the availability of high-quality data is often a

prime determinant of whether an income- or expenditure-based family resource definition is

used.” Our view is that both income and consumption are needed to determine accurately the

trend in inequality and economic well-being. If income and consumption inequality trends

agree, then we can have more confidence in the conclusion and if the trends diverge, then we

have directions for further research.

Two additional reasons to use income and consumption are the hump-shaped age-income

profile and potential measurement error in income and consumption. First, the hump-shaped

income and consumption profile reflects the LCPIH, with income rising until middle age and

then falling, and consumption following a similar, although less pronounced, hump-shaped

pattern. With these patterns, younger ages have consumption greater than annual income (and

greater than the average lifetime income), which suggests that consumption is a better proxy for

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unobserved permanent income. Similarly, older ages consume more than their annual income,

again suggesting that consumption is a preferred measure. Second, if there is measurement error

in income, for example, for the self-employed, consumption may be a better proxy for permanent

income at all ages (assuming no measurement error in consumption). However, if consumption

is underreported, for example, among the high income households (that motivates the

methodology of Aguiar and Bils (2010) and Attanasio, et al. (2012)), then income may be a

better proxy for permanent income assuming there is no measurement error in income.

Appendix A provides examples that show the importance of income and consumption in

measuring economic well-being. That appendix also provides examples that show that the

choice of income or consumption as a proxy for permanent income depends both on the

circumstances of the household and on the quality of survey data. A problem with using cross-

sectional data is that the data do not reflect the lifetime pattern of either income or consumption,

but reflect rather an annual snapshot of either (or both).

We show that both income and consumption provide information about the distribution of

household resources and the trend in inequality over time. The maximum amount of income and

consumption may provide an upper bound on household resources and both the maximum and

minimum may provide bounds on the “true” level of economic resources and its distribution. If

all four measures demonstrate similar trends, then one can be more confident of the actual trend

in inequality.

What are income and consumption and how are they measured?

To compare well-being using income and consumption measures and to use them

together in our maximum and minimum approach, income and consumption must be constructed

using a consistent framework. The most comprehensive concept of income and consumption is

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drawn from the suggestions of Haig and Simons. Haig (1921) stated that income was "the

money value of the net accretion to one's economic power between two points of time," and

Simons (1938) defined personal income as "the algebraic sum of (1) the market value of rights

exercised in consumption and (2) the change in the value of the store of property rights between

the beginning and end of the period in question."

Economists have used the equation that income (Y) equals consumption (C) plus the

change in net worth (W) as the working definition of Haig-Simons income. In an attempt to

relate all three components, the new Canberra Group Handbook on Household Income Statistics

(2011) states, “Household income receipts are available for current consumption and do not

reduce the net worth of the household through a reduction of its cash, the disposal of its other

financial or non-financial assets or an increase in its liabilities.” Similarly, the Systems of

National Accounts defines household income as “…the maximum amount that a household or

other unit can afford to spend on consumption goods or services during the accounting period

without having to finance its expenditures by reducing its cash, by disposing of other financial or

non-financial assets or by increasing its liabilities.” However, no studies use this definition to

the fullest extent.5 No household survey has the necessary variables to create a full measure of

Haig-Simons income. Most studies of income include the money income but do not examine

changes in asset values and only a few examine the impact of capital gains (e.g. CBO (2011),

Piketty and Saez (2003), and Smeeding and Thompson (2011)).

Using the equation, Y = C + W, income and consumption are directly related; the

measurement of income depends on the extent to which it is used for current consumption. Once

income is determined using the Haig-Simons definition, consumption can be obtained as income

5 Smeeding and Thompson (2011) discuss the Haig-Simons income measure and construct a “More Complete

Income” measure that attempts to account for the realized and unrealized returns on asset income.

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less the change in net worth. Incomplete measure of income and wealth, however, can make

measuring consumption difficult.

While consumption is usually measured with observed expenditures (with adjustments

for the service flows from housing and durable goods), the change in wealth is composed of

changes in observed wealth (as in changes in savings, interest, etc.) and unobserved wealth

(unrealized capital gains, stock price gains, and house value gains). Increases in observed wealth

could yield increases in income and/or consumption. If the observed changes are not included in

income (e.g., capital gains), then the residual changes in consumption will not match the changes

in income. This measurement error is only magnified with unobservable changes. While

interest, dividends, rents and royalties are measured, many other items (e.g., capital gains,

imputed returns on retirement assets) are not included, and depletions in (or additions to) savings

are also excluded.6

Perri and Steinberg (2012) provide the following example: “Consider two households

with the same income but very different shocks to the value of their wealth. Looking only at

income would not inform us about distributional changes between them, but looking at

consumption would, as the households would adjust their consumption in response to changes in

their net wealth. More concretely, when housing prices fall, households feel less wealthy and

spend less—even when their salaries and other income streams do not change.” Alternatively,

increases in house prices can have a wealth effect causing households to increase spending.7

As a result, measured consumption can become uncorrelated with measured income, and

fluctuations in consumption can be independent of fluctuations in income. If income and

6 Smeeding and Thompson (2012) attempt to measure a “More Complete Income” by imputing the value of interest

received on wealth, as well as include both realized and unrealized capital gains. 7 Lovenheim (2011) finds strong evidence that the increases in home values in the mid-2000s led to much higher

expenditures on education.

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consumption are consistently and completely measured, then the difference between income and

consumption will be the change in wealth, and deviations in Y-C will be given by the

unmeasured changes in wealth. If income and consumption are measured with error, then the

changes in wealth can exacerbate this measurement error.

Our goal is to have measures of disposable income and consumption that are accurate and

as closely linked as possible (given the data limitations) to compare their annual changes and

distributions and to obtain a resource measure that best reflects the annual level of the economic

well-being of households. While there may be reasons to exclude education, medical care or

durable goods from the measurement of consumption, removing these items from consumption

distorts the relationship between income and consumption. Removing these items from

consumption, while leaving income unadjusted, especially distorts the relationship between

income, consumption, and the change in net worth. It may also bias the measurement of

consumption in equality if high income households are more likely to spend on durables such as

expensive automobiles or home electronics or spend large amounts on elective medical

procedures or college education for their children.

The CE Survey Data

We use the only data set in the United States that contains both income and consumption-

expenditure information, the CE Interview Survey data, to compute measures of consumption

and income inequality. The CE survey has been a continuing quarterly survey since 1980. Data

are collected from consumer units8 five times over a 13-month period. The second through fifth

interviews are used to collect expenditures for the previous three months; for example, a

8 A consumer unit comprises members of a household who are related or share at least two out of three major

expenditures--housing, food, and other living expenses. A person living alone is a single consumer unit. While the

terms consumer unit and households are used interchangeably in this paper, there are households consisting of more

than one consumer unit; approximately 3 percent more consumer units than households.

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consumer unit that is visited in March reports expenditures for December, January and

February.9

We begin our analysis in 1985 as this is the first year with the most consistently

comparable data over time. Although the continuous CE Survey began in 1980, all variables

were not consistently collected between 1980 and 1984 (e.g., rental equivalence) and the sample

excluded rural households in 1982 and 1983. In addition, as mentioned above, much of the

increase in consumption inequality occurs in this early 1980-1984 period, which could be the

result of the changes in the CE Survey.

We examine four different resource measures: income, disposable income, expenditures,

and consumption. Income is the money income from employment, investment, government

transfers, and inter-household transfers of money. Disposable income is money income, plus the

value of food stamps and federal tax credits less the cost of federal and state income taxes and

FICA taxes. Expenditures are spending on all goods and services for current consumption, but

excluding life insurance, pensions, and cash contributions. Consumption is total expenditures

minus the purchase price of vehicles minus the expenditures for home-ownership plus the service

flow from vehicles plus the reported rental equivalence of home-ownership plus the value of

federal government rental assistance. As with other research on consumption, we do not include

goods obtained through barter, home production, or in-kind gifts from other households or

organizations. In contrast to other research, however, our measure of consumption includes all

other components of consumption-expenditures that are used for current consumption, and does

not exclude education, health care expenses or other durable goods. The specific techniques

used to create our consumption and income measures are discussed in appendix A.

9 The first interview is used to “bound” the interview and prevent reporting of expenditures in the wrong time

period. Data reported in the first interview are not released nor used in any estimation.

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Although our measures of income and consumption do not use the complete Haig-Simons

definition, we provide a more complete measure of consumption than previous research that is

better linked to disposable income in order to more fully capture the levels and trends in the

distribution. These measures include the income used to purchase current consumption,

excluding only capital gains and the depletion of savings, and the consumption measure attempts

to capture all current consumption. As a result, disposable income and consumption are in

balance and in the spirit of the Haig-Simons identity.

To match the income and consumption for each household and obtain annual measures of

consumption, we only use those consumer units who participated in the survey for all four

expenditure-interview quarters. In this manner, we obtain the income and consumption for the

same 12-month period. We do not restrict our sample by age, tenure or income reporting status.

Previous papers restricted their samples to “complete income reporters” as defined by the CE

Survey. Fisher (2006) finds that incomplete income reporters have lower consumption than

complete income reporters, which may affect any conclusions about the level of and trend in

inequality.

The CE Survey began imputing income in 2004 but did not impute previous years. We

replicate the BLS methodology as closely as possible and impute all income for 1985-2010, and

therefore, we do not restrict our sample by income reporter status. See Appendix B for a

detailed description of the imputation methodology.10

We present evidence below comparing the

distribution of our imputed income to the CPS.11

By imputing income, we treat the income data

the same way the consumption data are treated, as the consumption data are also imputed in the

10

We impute five implicates. At the moment we use the mean of the five implicates as our estimate of income.

Using mean income lowers the level of inequality but the trend in inequality is the same if we used the five

implicates and adjusted the measure for multiple imputation following Rubin (1987). 11

See figure A5 for a comparison to the income distribution in CPS.

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CE Survey; while previous research has removed incomplete income reporters, no previous

research has removed incomplete consumption reporters.

As the households who remain in the sample for four quarters are more likely to be

homeowners and older households, we follow the procedures in Sabelhaus (1993) and Fisher and

Johnson (2006) to re-weight the sample to represent the quarterly sample. For after-tax income

we use the National Bureau of Economic Research’s (NBER) TAXSIM program (see Feenberg

and Coutts (1993))12

to estimate federal, state and FICA taxes and tax credits such as the Earned

Income Tax Credit. All values are equivalized using the square root of household size (see

Buhmann, et al. (1988)) and the weights are adjusted to reflect person weights. Finally, all

values are adjusted to 2010 dollars using the CPI-U-RS.13

Table 1 shows the means for these resource measures over time, which shows that they

all increase during the 1985-2010 period. As Table 1 indicates, there is a convergence between

income and disposable income, which suggests a decrease in the average tax rate (ATR) during

this period. Similarly, the increased gap between disposable income and consumption indicates

a falling average propensity to consume (APC). The fact that consumption is almost always

lower than expenditures suggests that the service flow from vehicles and the rental equivalence

value of home-ownership are lower on average than the spending on these items (and the

imputed value of subsidized housing has a relatively minor impact on the overall means). The

main impact of using consumption is that it produces a tighter distribution and lower inequality

than using expenditures.

IV. The levels and trends in inequality

12

http://www.nber.org/taxsim/. See Appendix C for a description of how taxes were estimated using TAXSIM. 13

Others suggest that this is an over-estimate of inflation (see Meyer and Sullivan (2011) and Broda and Romalis

(2009), Gordon and Dew-Becker (2009) and Johnson (2004)).

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Figure 1 shows the staircase pattern of changes in the income and consumption

distributions between 1985 and 2005. All measures demonstrate an increase in inequality, with

the top quintile obtaining the largest increase in all resources during the 1985-2005 period. As

the figure shows, however, the CPS income shows a larger step for the top quintile than the other

quintiles (and hence, indicates a larger increase in inequality). Turning to the most recent five

years, we find a slightly different pattern. While all of the income measures show a negative

staircase pattern (all quintiles experienced decreases in resources, with the top quintile

experiencing the smallest decrease), consumption is more stable across quintiles and reflects the

picket fence pattern.

To obtain a summary measure of these changes in inequality, we use the Gini index. The

Gini index is the most commonly used measure of inequality and satisfies all of the key

properties of an inequality index, including the important principal of transfers (see Sen (1997)).

Many previous studies use the variance (or standard deviation) of logs; however, this measure

does not satisfy the principal of transfers; it is a consistent measure of inequality only for log

normal distributions.

Similar to previous work and consistent with the LCPIH, the levels of consumption

inequality (using the Gini) are slightly lower than those for income (and as shown in figure A3

the distribution of consumption dominates (in the second order) that for income). The trends,

however, are similar during the 1985-2010 period.

Figure 2 shows the Gini index for income, disposable income, expenditures, and

consumption and compares these to the Gini obtained using income from the CPS.14

As shown,

14

The CPS data changed the collection methodology in 1994 to computer-assisted data collection and adjusted the

income reporting limits. To account for these changes, following Atkinson, et al. (2011) and Burkhauser, et al.

(2012), the Gini coefficient for 1993 is set equal to that in 1992 and all previous years are adjusted by the same

factor.

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the CE income Gini shows similar trends as the Gini index for income in the CPS data, with

fairly close end points in 1985 and 2010. While the Gini for income using CPS data increases

7.5 percent between 1985 and 2010, the CE income Gini increases 11.2 percent; however, the

CE income Gini is more volatile because of the smaller sample size in the CE survey (as

compared to CPS).

Figure 2 and Figure 8 show that disposable income inequality and consumption

inequality track each other between 1985 and 2005 (and for all years between 1997 and 2006),

but diverge during the past five years. Between 1985 and 2005, consumption inequality

increases 9.4 percent, while disposable income inequality increases 7.5 percent. Over the entire

25-year period, however, disposable income inequality increased 9.9 percent, while consumption

inequality increased 6.6 percent (about two-thirds of the increase in income). Due to the smaller

sample sizes in the CE, however, these estimates are highly volatile and the standard errors are

large.15

But note also that one can obtain different summary results depending on the years

chosen as starting or end points.

Inequality in the Great Recession

An interesting aspect of Figure 2 is the behavior of the inequality around the period of the

Great Recession, from 2005 to 2010. As was demonstrated above in Figure 1, consumption

inequality is basically unchanged over the past 5 years, and the Gini coefficients confirm this

result. Prior research focused on the period from 2006-2009 and showed a fall in consumption

inequality coupled with a rise in income inequality, and no change in disposable income

inequality. Heathcote, Perri and Violante (2010) extend their previous results to 2008, and find

15

Because of the small sample size in each year, the standard errors are large. We construct a moving average of

data (using years of data for each year, e.g., all households in 1990 and 1991 for the 1991 calculations). This

method yields similar levels and trends in inequality, and standard errors that provide significant changes between

1985 and 2005 (calculations are available from the authors). Future work will bootstrap the standard error of the

Gini coefficient and provide confidence intervals for all estimates.

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that consumption inequality peaks in 2005 and then steadily falls in 2006, 2007 and 2008. Petev,

Pistaferri, and Eksten (2011) also find that inequality falls during 2007 and 2008, and Attanasio,

et al. (2012) find a fall between 2005 and 2010. Finally, Perri and Steinberg (2012) find that

inequality changed very little from 2006 to 2010 using two measures, the ratio of the 95th

to the

50th

percentile and the ratio of the 50th

to the 20th

percentile.

Heathcote, et al. (2010) claim that their paper “…reveals surprising dynamics for

consumption. The reason why consumption inequality declines, is a substantial fall in spending

at the top of the consumption distribution, while spending at the bottom increases.” And they

point to Parker and Vissing-Jorgenson (2009) who state “Given the large exposure of high

income and high consumption households to movements in aggregate income and consumption,

we expect recent poor aggregate economic performance to reduce inequality.” Similarly, Dynan

(2012) finds that consumption fell more for higher income households during the Great

Recession, and Hurd and Rohwedder (2011) finds similar falls for stock holders, who are largely

high income households.

Figure 2 similarly shows a fall in consumption inequality between 2005 and 2008, but

then an increase to 2010 back to the 2005 level. This is coupled with a fairly continuous rise in

income inequality between 2005 and 2010. As suggested by Heathcote, et al. (2011), it is the

increase for the 10th

percentile together with the fall for the 90th

percentile that drives these

changes in consumption inequality between 2007 and 2009 (Table 2 shows the 10th

and 90th

percentiles). However, these changes must be placed in context of the entire period, which

shows consumption inequality fluctuating (mainly due to small sample sizes). Figure 2 shows

that this downward trend is reversed in 2009 and 2010, with consumption inequality in 2010

returning to the about the same level as in 2005.

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Higher income households are expected to have better tools, and sufficient wealth (or

“buffer” wealth), to smooth their consumption during periods of lower income; however, during

the Great Recession, they lost a large fraction of their wealth. Hence, to restore their buffer

wealth, these individuals may have needed to save more, which would decrease their

consumption growth. Further research will examine the impact of the recession and the resulting

period following the recession on these outcomes.

Comparison to previous research

Finally, we can compare our results to recent estimates of Heathcote, et al. (2010), Meyer

and Sullivan (2009), Attanasio, et al. (2012), Coibion, et al. (2012) and Hassett and Mathur

(2012). In all cases, our estimates of their consumption measures demonstrate increases in

consumption inequality that are similar to our results in Figure 2. Figure 3 shows that our

measure of non-durable consumption matches the measure in Heathcote, et al. (2010) and

increases 10.2 percent between 1985 and 2005 compared to their increase of 12 percent. 16

However, using our data to replicate the measure of core consumption in Meyer and Sullivan

(2009) yields an increase in the ratio of the 90th

and 10th

percentiles of 15 percent between 1985

and 2005, compared to a 2 percent fall in their measure (and compared to an increase of 21.6

percent for our consumption measure; see Figure 4).17

Attanasio, et al. (2012) find that the inequality of non-durable expenditures increases only

slightly in the CE Interview Survey, but increases much more so using the CE Diary Survey

(similar to the results found in Attanasio, et al. (2006)). They find that between 1985 and 2005,

the variance of the log of non-durable consumption increases about 3.5 percent in the CE

16

The Gini coefficients for Heathcote, et al. (2010) are obtained using their data set posted at

http://ideas.repec.org/c/red/ccodes/09-214.html 17

Core consumption is defined as food at home, rent plus utilities, transportation, gasoline, the value of owner-

occupied housing, rental assistance, and the value of owned vehicles. Note that the changes between 1990 and 2008

show a similar fall of 7%.

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Interview data, and about 9 percent using CE Diary data (basically 0.02 and 0.07 log points).18

Using a measure of non-durable spending in Heathcote, et al. (2010), we find an increase in

inequality of about 12 percent between 1985 and 2005 (using the variance of log inequality

measure). Attanasio, et al. (2012) also claim that income inequality from the Panel Study of

Income Dynamics (PSID) increases about 20 percent and that non-durable consumption from the

CE Interview Survey increases about half that amount. They use the variance of the log

difference between food at home and entertainment expenditures to better reflect changes in the

consumption of these items. Using this alternative measure, the increase using the Interview data

is closer to the increase using the Diary data. However, as with our measures, all of their

estimates show a smaller increase in consumption inequality than in income inequality.

Coibion, et al. (2012) use a measure of monthly consumption to examine the volatility.

Their Figure 1 shows that the Gini for after-tax income increases about 6.0 percent between 1985

and 2005, while the Gini for consumption increases 5.4 percent. Finally, Hassett and Mathur

(2012) claim that consumption inequality has remained stable for the past 25 years. However,

their Figure 1 and Figure 4 show a slight increase in consumption inequality between 1985 and

2005. By approximating the data in their Figure 4 we find that consumption inequality (at the

Consumer-Unit Level) increased about 8.5 percent between 1985 and 2005.

V. Measurement Error

Many recent studies demonstrate the presence of underreporting of both income and

consumption in household surveys. BLS, in their cooperation with CNSTAT to conduct a panel

on redesigning the CE survey, stated: “From 1984 until the present, the ratios of aggregate

expenditure estimates from the CE compared with Personal Consumption Expenditures (PCE)

estimates from the National Accounts show a declining trend for a large number of spending

18

Changes are from Figures 6, 9, 11a, 11b in Attanasio, et al. (2012)

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categories, serving as evidence of underreporting.” Garner, et al. (2006) find that the ratio of CE

to PCE expenditures fell from 88 percent to 84 percent between 1997 and 2002, and published

tables by Passero (2011) that find the ratio remained fairly constant between 2003 to 2008.

Similarly, the results in Bee, et al. (2012) suggest a slight fall in the ratio of comparable

items from 82 percent in 1986 to 79 percent in 2010.19

They state that “…over the past three

decades there has been a slow decline in the quality of reporting of many of the mostly smaller

categories of expenditures….” They also suggest that the CE Interview survey “…does quite

well in terms of a high and roughly constant share of expenditures relative to the national

accounts for some of the largest components of consumption.” In contrast, Attanasio, et al.

(2012) claim that the “…Interview survey is plagued by some serious measurement problems.”

However, their conclusion is based on the same evidence presented in Bee, et al. (2012), along

with their results of the different inequality trends obtained using the CE Interview and CE Diary

surveys .

As shown in Bound, et al. (2001) and Gottschalk and Huynh (2010), if measurement

error is classical, independent of income (or consumption), then an increase in error will increase

inequality. Gottschalk and Huynh (2010) generalize this result to non-classical measurement

error, which could cause a decrease in inequality. They show that the impact of measurement

error on inequality can be represented by the sum of the covariance between the error and the

resource and the variance of the resource. They find that the difference between the variance of

mismeasured log earnings (or income or consumption) and the variance of actual log earnings

depends both on the variance of measurement error and the covariance of measurement error and

19

This ratio is calculated by aggregating the comparable items in Table 1b in Bee, et al. (2012)

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earnings. They state: “While larger variance of measurement error will unambiguously lead to

an upward bias in inequality, this will be offset by mean reversion in measurement error.”20

Hence, increased measurement error can imply an increase or a decrease in inequality of

the reported resource measure. According to Gottschalk and Huynh (2010) “…increases in

inequality will be overstated if the variance of the measurement error is increasing or if mean

reversion in measured earnings [or income] is declining.” If the measurement error is correlated

with income, such that higher income households are increasingly likely to underreport their

income (or consumption), then mean reversion in measurement error is increasing. If the

variance of the error is not increasing, the increase in measurement error can suggest that the

increase in inequality in the survey data is not overstated. It could imply that the increase in

inequality of the reported measure is even higher than the true measure of inequality.

This is the hypothesis made about consumption inequality in Attanasio, et al. (2012) and

Aguiar and Bils (2011). They suggest that higher income households are increasingly likely to

underreport their expenditures relative to lower income households, implying an increase in

mean reversion for expenditures (or consumption). They use an adjustment that causes

expenditures for high income (or expenditure) households to increase more over time, and they

find a larger increase in consumption inequality using their adjusted consumption than the

increase that occurs with the reported data. By using all individuals who have both income and

consumption, our results show that the CE Interview Survey provides evidence of a significant

increase in inequality in both income and consumption.

Even if these adjustments were justified, there is substantial evidence that underreporting

also exists in income (see Sabelhaus, et al. (2012)). Meyer, et al (2008) state: “We find that

underreporting is common and has increased over time…There is substantial variation across

20

And this can be applied to the Gini properties (see Yitzhaki and Schechtman (2011)).

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surveys, with the CE Survey typically having the lowest reporting rate and the SIPP having the

highest rate for most programs.”21

It is not clear how underreporting in both consumption and

income will impact the trend in inequality, or the relationship between income and consumption

inequality.

While Attanasio, et al. (2012) and Aguiar and Bils (2011) adjust consumption, they do

not attempt the same adjustment for the increase in income inequality. If underreporting is

present for both income and consumption, then comparably adjusted (or unadjusted) series must

be used to compare the trends in consumption and income inequality. As a result, in order to

compare the trends in consumption and income inequality in the presence of underreporting,

researchers must attempt to adjust both measures.

The Average Propensity to Consume

As stated by the NAS report, one of the main criteria in deciding whether income or

consumption provides a better measure of economic well-being lies in the quality of the data. As

discussed above, many studies document the underreporting in both income and consumption.

The issue is which measure contains more error.

One method to examine the different measurement errors in both income and

consumption is to use both in an estimation procedure (as in Gottschalk and Huynh (2010) and

Gallup (2010)). The correlation between these resource measures can provide a measure of the

difference and it provides a measure of the association between permanent and transitory

income. If the LCPIH holds, then higher correlation denotes a higher level of permanent income,

while lower correlation suggests more of an impact of transitory changes. As Figure A2

demonstrates, disposable income and consumption have a correlation coefficient between .65

21

Burkhauser, et al. (2012) claim, however, that “…users of both CPS and of IRS tax return data should be

comforted by our finding that…differences in estimates from the two data sources are relatively minor.”

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and .70 each year, and hence, transitory income changes are included in the measure of

disposable income.22

Another way to examine the differences is by looking at the average propensity to

consume – the ratio between consumption and disposable income. Figure 5 shows that, as

expected, APC falls with income, but this relationship is similar over time (see also Sabelhaus, et

al. (2012)).23

The issue is whether these high APCs at the low end of the income distribution

represent underreported income (as in Figure A1d) or whether the high APCs at the other end of

the distribution represent underreported consumption (as in Figure A1e). If these are data quality

issues, but the data quality is similar over time, then there may not be any implications for the

trends in inequality. Alternatively, these APCs may simply reflect the LCPIH (as in Figures A1a

and A1b).

Examining the characteristics of the high and low APC households may provide some

insight into whether the LCPIH applies or whether there might be measurement error concerns.

Table 3 shows some characteristics for these households. About 9 percent of people live in

consumer units with low APCs (under 0.5) and 10 percent have high APCs (over 2.0). The high

APC households are generally lower income (as seen in the scatter plot in Figure 6 and in Table

3), which include households who have income and consumption relationships that could be

similar to the LCPIH pattern. They are more likely to be older and single and could be at either

end of the age-profile pattern suggested by the LCPIH (see Figure 1a). In contrast, the low APC

households are higher income households and more likely to be other family types. While these

characteristics may suggest behavior consistent with the LCPIH, other statistics in Table 3

suggest there may be other issues with the data and the measures of consumption.

22

The Gini correlation (or Gini mobility index) similarly measures the relationship between these resource measures

and shows a similar consistency over time. 23

These results are similar across data sets (as in the PSID and HRS), see Dynan (2012).

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Table 3 also shows that it is more likely that the high APC households contain self-

employed people who are more likely to underreport their income (see Hurst, et al. (2010) and

Harris (1996)). The high APC households are more likely to report a decrease in their asset

holdings (checking, savings, and security accounts) and they are more likely to report increases

in credit card debt. In addition, these households are more likely to be homeowners without a

mortgage.

Developing the Maximum and Minimum measures

The patterns in Figure 5 and Table 3 suggest high levels of savings at higher incomes,

which are much higher than other estimates (see Sabelhaus, et al. (2012), and references therein).

The large consumption levels for some households with low incomes seem implausible. While

some of these can be explained by the characteristics of households, some of these APCs appear

too large or too small. As a result, consumption could suffer from a fair amount of mean

reversion, as Gottschalk and Huynh (2010) find for income in the Survey of Income and Program

Participation (SIPP).

Given the negative correlation between APC and income, the economic well-being of

many of the low income households may be more accurately represented by their consumption,

which may be consistent with the LCPIH. However, many of the high income households may

be more accurately represented by their income.

As we have maintained, both income and consumption provide information about the

distribution of resources and trends over time. Hence, using the maximum and minimum of both

provides another measure of well-being. As all measures are contaminated by measurement

error, additional information is useful. For example, Browning and Crossley (2009) show how

two noisy measures provide useful information about the structure of the measurement error.

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Gallup (2010) uses both measures to obtain the inequality of permanent income and finds that

the inequality of permanent income is lower than either income or consumption inequality.

Using the maximum (as opposed to the average or an integrated regression approach as in

Gallup (2010)) provides a simple method that can serve as an upper bound on household

resources. The purpose of using the maximum and minimum is that they could be bounds on the

true level of economic resources. Underreporting could exist for both income and consumption,

which would suggest that the true level of resources lies above both, but if all four measures

demonstrate similar trends, then one can be more confident of the actual trend in inequality and

years with differences can suggest data or measurement issues or that changes in wealth affected

inequality trends.

In evaluating the levels, if consumption Gini is less than the Gini for disposable income,

the correlation between income and consumption is positive, and APC decreases with income,

then the Gini for the maximum will lie between the Gini coefficients for income and

consumption, and similarly for the minimum (see Appendix D). This relationship is shown in

Figure 7.

As Figure 7 and Figure 8 show, the Gini for the maximum increases 13.7 percent

between 1985 and 2010, and the Gini for the minimum increases 3.6 percent (which bound the

increases in income and consumption of 6.6 and 9.9 percent). If increases in mean reversion

exist mainly for consumption by high income households, then using the maximum may yield no

changes in mean reversion. Hence, the trend in the Gini for the maximum may better reflect the

overall increase in inequality.24

VI. Conclusion

24

Again, there is something happening in the later years around the Great Recession. The Gini for the maximum

diverges more from the Gini for consumption during this period; this is the subject of future research.

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We present evidence on the level and trend in inequality over the last twenty-five years in

the U.S. using disposable income and consumption for the same sample of individuals from the

CE Survey. Our sample includes all individuals, not just those that live in urban areas or those

that are of working age. While consumption inequality is always lower than income inequality,

income and consumption inequality increase at approximately the same rate between 1985 and

2005. Over the entire 25-year period, consumption inequality increases by about two-thirds of

the increase in disposable income inequality. These results contradict much of the existing

research that finds that consumption inequality was relatively flat since the mid-1980s. Three

recent papers argue that the increase in consumption inequality mirrored the increase in income

inequality, but those papers make significant adjustments to the CE Survey data or impute

consumption in other surveys. Our straightforward approach uses the entire CE Survey sample

for both income and consumption and takes the consumption data as reported by the households.

While we impute income for those households that do not report valid values for all of their

components of income, the observed increase in income inequality in the CE matches the level

and trend found in the CPS, the standard data set used to measure earnings and income

inequality.

Examining income and consumption together using the same sample provides an

important contribution to the literature on the economic well-being of individuals. That the

trends in the two measures are nearly identical provides even more confidence in the results. We

also show estimates of permanent income inequality using the maximum and minimum of

income and consumption and find that the trend in inequality is approximately the same as seen

using income or consumption by itself.

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Tables and Figures

Figure 1: Percentage change in resource measure, 1985-2005 and 2005-2010

1985 - 2005

2005 - 2010

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Figure 2: The trends in income and consumption inequality using the Gini coefficient

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Figure 3: Comparing Heathcote, et al (HPV) (2011) measure of non-durables using Gini

coefficient

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Figure 4: Comparing Meyer and Sullivan (2009) measure of core consumption, using P90/P10

ratio

Figure 5: Average Propensity to Consume by disposable income level, 1990, 2000, 2005 and

2010

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Figure 6: Plot of consumption and disposable income, 2010

APC=0.5

APC=2.0

APC=0.5

APC=1.0

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Figure 7: The trends in inequality (Gini) using the maximum and minimum

Figure 8: Changes in inequality. Gini indexed to 1.0 in 1985.

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Table 1: Mean and Median Income from CE and CPS, and Mean Disposable Income,

Consumption and Expenditures from CE (in 2010$, using CPI-U-RS and equivalized)

Year

CPS

Median

Money

Income

CPS -

Mean

Money

Income

CE -

Median

Income

CE -

Mean

Income

CE

Disposable

Income

CE

Consumption

CE

Expenditures

1984 29,039 34,519 27,014 33,768 26,424 22,299 23,335

1985 29,515 35,123 27,746 33,353 26,114 23,461 24,229

1986 30,684 36,474 28,123 33,492 26,890 23,703 25,457

1987 31,571 37,258 28,022 34,030 27,571 23,782 24,730

1988 31,697 37,705 28,490 34,818 28,274 23,919 25,097

1989 32,300 38,499 29,647 36,362 29,334 25,001 26,005

1990 31,535 37,588 28,232 34,219 27,726 24,389 24,663

1991 31,056 36,998 27,511 33,918 27,371 24,425 25,076

1992 31,033 36,970 27,436 33,776 27,455 23,090 24,904

1993 30,523 37,018 27,982 33,967 27,615 24,016 25,458

1994 31,273 37,883 28,917 34,911 28,259 24,368 25,930

1995 32,043 40,841 28,793 34,956 28,392 24,092 25,397

1996 32,518 41,659 29,705 36,653 29,407 24,564 25,653

1997 33,523 43,185 31,151 38,021 30,515 25,697 26,451

1998 34,732 44,567 30,741 38,658 30,970 25,688 26,491

1999 35,632 45,158 32,325 41,106 32,647 26,266 27,378

2000 35,979 46,815 32,729 40,477 32,707 26,480 27,064

2001 35,558 46,506 33,539 41,505 33,560 26,723 27,132

2002 35,133 45,580 34,224 42,242 34,736 27,339 27,681

2003 34,993 45,523 33,084 41,822 34,773 26,995 27,378

2004 34,769 45,408 35,059 44,412 36,955 29,255 29,294

2005 35,104 46,066 34,445 43,711 36,189 29,801 29,352

2006 35,457 47,003 34,950 43,769 35,983 30,717 29,108

2007 35,937 46,470 34,117 43,388 35,632 29,270 28,642

2008 34,744 45,192 32,807 41,980 34,783 28,921 28,362

2009 34,039 44,824 31,717 41,184 34,531 27,895 27,201

2010 33,623 44,052 29,958 39,938 33,501 26,905 25,995

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Table 2: Medians, 10th

and 90th

percentiles for consumption and disposable income (DPI), (in

2010$, using CPI-U-RS and equivalized)

Year

Consumption

- P10

Consumption

- Median

Consumption

- P90

Disposable

income-

P10

Disposable

income-

Median

Disposable

income- P10

1984 9,418 20,654 36,500 8,873 22,722 48,546

1985 11,238 20,748 37,775 9,392 23,438 46,542

1986 9,771 21,303 38,910 8,644 23,764 48,976

1987 10,272 21,771 39,338 8,927 23,962 49,456

1988 10,264 21,670 39,106 10,183 24,540 50,330

1989 11,130 21,974 41,990 10,804 25,195 53,766

1990 10,359 21,623 41,386 8,864 23,977 49,732

1991 10,680 21,687 39,828 8,125 23,367 51,258

1992 9,940 20,300 38,333 7,705 23,591 51,165

1993 10,411 21,486 39,832 8,279 24,079 50,787

1994 10,883 21,858 40,644 9,373 24,455 51,148

1995 10,413 21,333 40,918 9,653 24,551 52,157

1996 11,061 21,728 40,564 8,889 24,959 51,814

1997 11,143 22,957 42,796 9,438 26,177 54,989

1998 11,213 22,554 43,609 9,368 26,447 57,491

1999 11,313 23,148 43,503 10,771 27,473 57,403

2000 11,806 23,413 44,269 10,745 28,162 58,267

2001 11,741 23,611 44,330 10,920 28,847 60,874

2002 12,129 24,640 45,282 11,461 30,322 62,161

2003 11,619 23,958 45,368 10,941 29,836 62,953

2004 12,103 25,554 48,984 11,418 30,973 67,494

2005 12,741 25,933 52,082 10,898 30,230 68,382

2006 12,611 27,145 51,784 10,726 30,411 66,028

2007 12,550 25,838 48,825 10,787 29,827 65,314

2008 12,991 25,673 47,381 10,032 28,957 65,146

2009 12,670 24,529 46,604 10,585 28,396 63,048

2010 11,402 23,510 44,882 9,745 27,394 63,329

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Table 3: Percent distribution for each APC level (person weighted), 2009-2010

All APC<0.5 APC≥2.0

Family typea

Married without children 21.7 27.7 14.6

Single person 27.3 14.7 50.6

Other family type 15.6 21.6 13.9

Single Parent 5.8 1.6 10.5

Homeownerb 66.0 72.5 56.1

with mortgage 41.2 50.8 20.6

without mortgage 24.8 21.7 35.5

Renter 34.0 27.5 44.0

Assets fell in last 12 month

Checking balance 13.9 11.3 16.8

Savings balance 18.6 15.5 18.1

Securities balance 34.4 29.6 33.4

Credit card debt increased in last 12 months 63.4 62.3 75.7

Ageb

Less than 35 22.6 20.9 23.4

35 to 45 18.4 19.6 9.5

45 to 55 20.9 23.8 16.6

55 to 65 17.7 22.0 19.4

65 and over 20.3 13.8 32.1

Self employed

Reference person 10.7 12.0 26.6

Spouse 10.6 12.3 23.0

Disposable Income distributionb

Bottom Quintile 21.8 6.6 83.0

2nd 18.7 5.3 12.6

Middle 19.6 8.6 3.6

4th 19.5 17.6 0.5

Top Quintile 20.2 62.0 0.2

Numbers represent the percent of characteristic in each APC level (e.g., 50.6

percent of people in Consumer Units with APC>2.0 are singles). a Not all family types are included. Family type does not sum to 100.

b May not sum to 100 due to rounding.

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Appendix A: Consumption and Income Measurement Issues

Defining Our Measures

To obtain an annual measure of consumption and income, we use consumer units who

participate in the survey for all interviews (representing about 75-80 percent of all consumer

units). Because young renters are under-represented in the sample of consumer units who

remain in the survey for all interviews, we use a procedure presented in Sabelhaus (1993) and

Fisher and Johnson (2006) to adjust the weights by age and housing tenure (homeowner/renter)

to obtain a better representation of the population. The consumer units are then placed in the

quarter in which their last interview occurred and the weights and household demographics are

those from the last interview. The data for a particular year are obtained by using all of these

four quarter CUs who had their last interview between the second quarter of one year and the

first quarter of the following year; for example, the data for 2009 consists of all households who

had their last interview between April 2009 and March 2010. Since the expenditures and income

are from the previous four quarters, the expenditures and income occurred between April 2009

and February 2010. Determining the years in this manner yields annual data from 1985 to

2010.25

We measure economic well-being by using two definitions of both income and

consumption. Similar to the Census Bureau definition of money income, we use pre-tax/post-

cash transfer money income; this does not include the value of food stamps or other in-kind

transfers.

The Consumer Expenditure (CE) Survey began imputing income in 2004 for those

respondents that refused to provide an exact dollar value and for those that did not know the

exact dollar value.26

Before 2004 these values are left as missing. We impute income for all

consumer units from 1985-2010, following the CE Survey’s methodology for imputing income

where possible. Appendix B provides the detail on our imputation methodology.

We also use a measure of “disposable income”, which is total income minus personal

income taxes (net of refunds including the earned income tax credit), personal property taxes and

payroll taxes plus the value of food stamps. We estimate income taxes and payroll taxes using

NBER’s TAXSIM program (Feenberg and Coutts, 1993), and estimate taxes for each of the five

income implicates.27

See appendix C for a description of the tax estimation. Figure A2

compares the imputed income series to the CE published income and CPS income.

We use two measures of consumption: expenditures and consumption. Expenditures are

defined as the amount that the consumer unit actually spends for current consumption. Spending

on items not actually consumed by the consumer unit is not included. Expenditures include

expenditures for food, housing,28

transportation,29

apparel, medical care,30

entertainment,31

and

25

Since there are only two quarters of data for the 1984 period, we do not include this year in our analysis. The

average sample size for each year is about 3000 consumer units. 26

The data CD provided the BLS includes documentation describing the official BLS imputation process. 27

http://www.nber.org/taxsim/ 28

Housing includes expenses associated with owning or renting a home or apartment, including rental payments,

mortgage interest and charges, property taxes, maintenance, repairs, insurance, and utilities. Expenditures for other

lodging and household operations are in the miscellaneous items category. Expenditures for principal payments for

mortgages are excluded. 29

Transportation includes expenditures for the net purchase price of vehicles, finance charges, maintenance and

repairs, insurance, rental, leases, licenses, gasoline and motor oil, and public transportation. Public transportation

includes fares for mass transit, buses, airlines, taxis, school buses and boats.

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miscellaneous items32

for the consumer unit. Excluded are expenditures for pensions and social

security, savings, life insurance, principal payments on mortgages, and gifts (of cash, goods and

services) to organizations or persons outside the consumer unit. Included are the purchase prices

of durable goods other than housing.

As the CE survey changed the method to collect food at home and food away from home,

we made some adjustments to insure comparability over time. The CE survey modified the

questionnaire between 1982 and 1987 for the collection of food at home. During these years, the

CU was asked for usual monthly expenditures on food, and since 1988 the CU has been asked

for usual weekly expenditures. As expected, using weekly expenditures and aggregating up to

annual expenditures provides larger food expenditures that using monthly expenditures. We

follow a procedure similar to Battistin and Padula (2009) and regress food expenditures on CU

characteristics (income, tenure, marital status, age and age squared, number of adults and

children) and a dummy for the years 1984-1987. We use the dummy to adjust all food

expenditures during these years by the same ratio – basically increasing these expenditures by a

factor of 1.2198. Similarly, in 2007, the CE changed the questionnaire regarding food away

from home. Before the 2nd

quarter of 2007, CUs were asked for usual monthly expenditures and

currently, the CU is asked for usual weekly expenditures. We use a similar procedure to adjust

all food away from home expenditures by the same amount – basically increasing these

expenditures by a factor of 1.565 for all years before 2007 (2nd

quarter).

To obtain our measure of consumption, we estimate the service flows of homeownership,

cars and trucks. For the value of homeownership, we use the reported rental equivalence value

obtained from the consumer unit. Consumer units who own their home are asked, “If someone

were to rent your home today, how much do you think it would rent for monthly, unfurnished

and without utilities.” The annualized value of this is then used for homeownership cost in place

of the amount used in the definition of expenditures. In addition, we calculate the imputed value

of government rental assistance. Following a procedure similar to Meyer and Sullivan (2008),

we regress the rent (in logs) on the characteristics of the rental units, including number of rooms,

bathrooms, bedrooms and the squared values, the age (and age-squared) of the unit, whether the

unit is detached, a multi-unit building or a mobile unit, whether the unit has a swimming pool,

off-street parking, and the state and type of metro area. We estimate this on a rolling sample

using three years of data and then use the imputed value for CUs in public housing or rental

assisted housing if the imputed rent is higher than the reported rental cost.

For cars and trucks, we follow a process similar to that used in Danziger et al. (1982) and

Slesnick (1994) and estimate the service flow of durable goods by the change in the value of the

durable. Using the purchase price, P0, and the age, s, of the vehicle, the service flow, S, is given

by:

(1) St = (r + )(1 - )sP0,

where r is the interest rate and is the depreciation rate. We assume that r = .05 and = .1. The

CE Survey collects data on the ownership of vehicles, including the age and make and/or model

type. While the age and model type are asked of all consumer units, the purchase price is asked

only of those households who are currently financing their automobile (or who recently

30

Medical care expenditures are for out-of-pocket expenses including payments for medical care insurance. 31

Entertainment expenditures are for fees and admissions, televisions, radios, sound equipment, pets, toys,

playground equipment, and other entertainment supplies, equipment and services. 32

Miscellaneous expenditures are for personal care services, reading, education, tobacco products and smoking

supplies, alcoholic beverages, other lodging, and house furnishings and equipment.

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purchased the vehicle). Since many of the consumer units have missing values for the purchase

price, we imputed values based on the make and year, whether the vehicle was purchased new or

used and whether the vehicle had automatic transmission. Since most of the vehicles had their

make reported, we sorted the data by model type and whether the vehicle was new or used and

obtained the mean value of the purchase price for each cell. If there were no observations for a

particular cell or the type was missing, we then used the mean values by year, based on whether

the vehicle was new or used, a car or a truck and automatic or manual transmission. Using these

service flows, consumption is given by consumption-expenditures less the purchase of vehicles

and major appliances and the costs of homeownership plus the rental equivalence of owned

home and plus the service flows from cars and trucks.33

We use equivalent resource measures by dividing the household resources by the

constant-elasticity equivalence scale ((family size).5

). Inequality is then calculated using the

equivalent resources and weighting by family size times the household’s sample weight. Figure

A3 provides a more detailed picture of the correlation between disposable income and

consumption. Table A1 classifies individuals in households by their income and consumption

quintile and shows that many households are classified in different quintiles.

Income and Consumption as Complements

The following examples demonstrate the complementary nature of these two measures of

economic well-being, consider a standard age-resource profile based on CE data by age (see

Figure A1a). Assuming that the unobserved permanent income is simply the average lifetime

income, a standard LCPIH situation of either an elderly household who is depleting savings or a

young (possibly student) borrower can illustrate the LCPIH. At a young age consumption is

greater than annual income (and greater than the average lifetime income). Here, the LCPIH

suggests that consumption is a better proxy for unobserved permanent income. A similar

situation might occur in old age where again consumption is closer to permanent income than

current income. In older ages, although both consumption and current income are below

permanent income, consumption still yields a better measure of permanent income. Figure A1b

simply shows that the LCPIH suggests that the household will attempt to smooth out short-run

fluctuations in income, again suggesting that consumption is a better measure of permanent

income.

Figure A1c shows that although the household’s income fluctuates, the household

becomes accustomed to a certain consumption level. At the particular point in time (shown by

the line), this household could be a creditor borrowing heavily from his/her credit cards (or other

unsecured debt). Federal Reserve Governor Lindsey (1996) discussed this increase on debt

reliance, when he suggested that “households may be adding debt in order to sustain desired

consumption levels which cannot be justified by their earnings.” Here, consumption is greater

than annual income which is greater than (or less than or equal to) permanent income and

consumption is not a good measure of unobserved permanent income, but annual income,

although not always perfect, is a better measure.

Figure A1d illustrates the common problem of income being underreported in household

surveys. Many suggest that income for the self-employed is poorly reported on most household

surveys (see Hurst, et al. (2010) and Harris (1996)) and that using annual reported income may

33

This measure of consumption may still underestimate actual consumption since it does not include all in-kind

transfers, gifts received from other households, or the service flows from other durable goods, e.g., televisions,

recreational vehicles, and some luxury goods.

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not fully reflect the economic well-being of these households. In this example, at the line,

consumption is greater than permanent income, which is greater than reported income. As a

result, current consumption, rather than reported income, might be a better measure of permanent

income.

Figure A1e illustrates a problem with consumption data. Aguiar and Bils (2011) suggest

that higher income households underreport their expenditures on “luxury” goods. It could be

that with large (and permanent) increases in income, the household underreports their actual

consumption.

Figure A1a: Age profiles for disposable income and consumption using CE data

Figure A1b: Smoothing consumption over short-run income fluctuations

Consumption

Income

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Income

Consumption

Figure A1c: Excessive consumption in response to falling income

Figure A1d: Income underreporting

Figure A1e: Consumption underreporting

Consumption

Reported Income

Income

Reported

Consumption

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Appendix B: Imputing Income

We impute income sources for consumer units that reported receiving the income source

but failed to provide a valid value. Our imputation methodology follows the CE Survey’s

methodology as closely as possible. This appendix describes our methodology and where our

methodology differs from the methodology used by the CE Survey.

We impute any income variable with an invalid nonresponse flag or a “don’t

know/refuse” flag. Twelve family-level income variables are imputed: interest income; pensions

and annuities; financial income (e.g., dividends and royalties); alimony; child support; lump sum

payments; unemployment; food stamps;34

welfare; net income or loss from roomers or boarders;

net income or loss from other rental units; and, other income (e.g., cash scholarships and cash

stipends). Prior to third quarter of 1993, alimony and child support were combined in one

variable. The two sources are treated separately when feasible, given the methodology described

below. We impute lump sum income,35

while the CE Survey does not. In the official CE

definition of before-tax income, lump sum income is not included, and the CE only imputes the

components of before-tax income.

Five member-level income variables are imputed: wage and salary; Supplemental

Security Income (SSI) benefits; income or loss from the member’s own farm; income or loss

from member’s own nonfarm business; and, social security and railroad retirement income. We

differ from the CE’s treatment of social security and railroad retirement income. The CE Survey

imputes the last payment received for these items, and whether Medicare premiums were

subtracted from the last payment. It then multiplies that amount by the total number of payments

received over the previous twelve months, if a valid value is not provided. We instead impute

social security and railroad income earned over the previous twelve months. We ultimately are

interested in the income over the last twelve months and do not need to know the three

intermediate inputs.

The CE Survey introduced income bracket variables in the second quarter of 2001. If the

respondent refused to provide an exact dollar value for an income source, the respondent was

asked to provide an answer from a bracketed range. From 2001-2003, the respondent was given

the mid-point of the bracket as the dollar value for income for that source. Since 2004, the CE

Survey imputed the value for the bracketed income responders but restricted the imputed value to

be within the bracket. We differ from the CE Survey and continue to use the mid-point of the

bracket.

The CE Survey also imputes income for a portion of the consumer units that report valid

blanks for each and every income source listed above, excluding lump sum income.36

The CE

Survey refers to these consumer units as ‘all valid blanks’ (AVB). Approximately 2.2 percent of

all consumer units are classified as AVB. The income questions are at the end of the survey, and

the CE Survey is worried that some respondents may report no income as a way to end the

34

From 2001Q2 on, the food stamp question included food stamps and electronic benefits. The variable changed

names as well at that time. 35

Lump sum income includes lump sum payments from estates, trusts, royalties, alimony, prizes, games of chance,

and payments from people outside the consumer unit. 36

Before 2001Q2, the food stamp flag did not allow for valid blanks. Instead the consumer units were given a zero

for the food stamp variable, and the flag indicated a valid value. We impute for those with a $0 response for food

stamps before 2001Q2 because it is actually missing.

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survey. It is believed that some consumer units may truly have no income from any of these

sources.

As part of income imputation, the CE Survey imputes whether the AVB consumer units

were actually valid blanks. A predicted likelihood of receipt is estimated for each income

source.37

Among valid reporters, the dependent variable equals one if the consumer unit or

member received the income source and zero otherwise. The same independent variables are

used in the AVB process as the imputation process, as described below. After logit estimation

among the valid reporters, an out-of-sample likelihood is estimated for each AVB consumer unit

or member. Then a random number is generated for each AVB consumer unit or member for

each income source. If the predicted likelihood of receipt is greater than or equal to the random

number, the valid blank for that source is changed to an invalid blank. All invalid blanks

generated from the AVB process are then treated like any other invalid blank and are imputed for

that source. An AVB consumer unit could remain AVB, or it could have food stamps imputed

and nothing else imputed.

Methodology

The data are multiply imputed following the basic method of Rubin (1987). In brief,

coefficients are estimated using the valid reporters. The estimated coefficients are then shocked,

and the shocked coefficients are used to estimate a predicted value for the invalid reporters. The

predicted value is also shocked to arrive at the final reported value. Five implicates are

generated for each income source. In practice we use the Stata mi impute command. Rather than

use Ordinary Least Squares to generate the coefficients, we use predictive mean matching, which

matches the missing value with the mean of its nearest neighbors. All models are weighted. All

data are in real 2010 dollars when imputing.

Variables

The dependent variable equals the transformed level of the income source for all valid,

non-zero respondents. The CE Survey transforms the income source by subtracting its median

from all valid reporters. The variables are transformed before the model is run, and the

implicates are untransformed after model estimation.

A large list of independent variables is included in each model. We use the following

continuous variables: quadratic in age;38

transformed total expenditures (ERANKMTH);39

and, a

37

The AVB process is not done for wage and salary income, farm income or loss, and nonfarm business income or

loss. If someone reports being employed but fails to report wage and salary income, the respondent has an invalid

blank. If someone is not employed, the individual has a valid blank. Thus there can be no invalid blanks for wage

and salary income. Similar logic applies to farm and nonfarm income. 38

For the family-level variables, the individual-specific (e.g., age, race) demographic characteristics are for the

reference person. For the member-level variables, the individual-specific demographic characteristics are for the

specific member. 39

The variable is transformed using the same methodology as the transformation of the dependent variables. The

variable ERANKMTH does not exist on the public use files before the second quarter of 1994. The CE Survey

office provided us with the variable from 1987 to the first quarter of 1994. It also provided us with the values for this

variable from 2004-2006 because the value on the file in these years is affected by imputation. From 1984 to 1986,

we calculated the value for ERANKMTH from the MTAB file.

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quadratic time trend. For the member-level income sources, we also include usual hours worked

and weeks worked over the last fifty-two weeks.

We use the following categorical variables in the family-level model: race;40

education;41

urban/rural status; number of earners in the consumer unit;42

occupation;43

family type; region;

household tenure;44

and, a series of dummy variables for receipt of all other individual income

sources. When imputing unemployment insurance, welfare benefits, and food stamps, we also

include state dummy variables to capture variation in these programs across states. The member-

level models also include gender; marital status; and, relationship to the reference person (e.g.,

spouse, child). The model for wage and salary income also includes whether the member

contributed to an IRA/401(k)-type retirement plan in the last twelve months and whether the

member’s employer or union contributed to a pension plan for the member.

The CE Survey used backward induction to limit the number of independent variables

included in the final model. The model runs with all variables, but variables whose coefficient is

not statistically significant at the 15 percent level are removed. The model is run again on this

limited set of variables. If any variables are no longer statistically significant at the 15 percent

level, they are removed. This process continues until all variables remain statistically significant

at the 15 percent level. We do not follow this process. We use all variables at all times. Although

the variables are not statistically significant at some relatively low level, the variables

presumably provide some useful information and are correlated with the dependent variable.

We bottom code at $1 any income source that is imputed to be negative or zero if the

income source is not allowed to be negative.

The Sample

Following the CE Survey methodology, we use the current quarter and the previous

nineteen quarters of data to impute. This only becomes a problem in the early years of our data

where we do not have nineteen previous quarters available. From 1985Q3-1988Q4, we use the

twenty quarters before 1988Q4 to impute income for all of these quarters.

We only use those that appear in the fifth interview, as we are interested in only those consumer

units that complete all five interviews. The income questions are also only asked in the second

and fifth interviews. The CE Survey imputed by family type (e.g., husband and wife with the

youngest child under the age of 6; single males; single females), while we do not. Instead we

include family type as an independent variable.

40

Member-level race separated Asians from Pacific Islanders in 2003Q1. To remain consistent, we grouped Asians

and Pacific Islanders together in all years. Also in 2003Q1, race of the reference person included an additional

category for ‘multiple races.’ This was left as is as there was no way to recode to make the race variables agree. 41

Five categories were created education: less than high school; high school; some college; college; and, graduate

degree. 42

Four categories were created for number of earners: 0, 1, 2, and 3+. 43

Additional occupation categories were included starting in 1994. The categories were collapsed to match the

earlier data. 44

An additional category was added to tenure to create a separate category for those in public housing or subsidized

housing. The CE Survey kept public housing and subsidized housing as separate categories.

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Figure A2: CE and CPS published income and CE published expenditure data (2010$)

compared to our imputed income and expenditures

Table A1: Transition Matrix, Disposable Income and Consumption, 2010

Income

2010 Bottom 2nd Middle 4th Top

Bottom 59% 29% 8% 3% 1%

2nd 23% 34% 30% 10% 2%

Middle 10% 21% 31% 30% 8%

4th 5% 10% 21% 36% 28%

Top 3% 5% 10% 20% 62%

Consumption

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Figure A3: Correlation between disposable income and consumption, and sample size

Figure A4: Density functions for income and consumption, 2010

0 1 2 3 4 5 6

0.0

0.5

1.0

1.5

2.0

US Dollars x 100,000

Den

sity

Income

Consumption

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Figure A5: Comparison of the distribution of CE income, our imputed income, and CPS income,

2006

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Appendix C: Estimating Income Taxes

Income taxes are estimated for all consumer units, even those that report valid values for

some or all of their income taxes. Response rates to the tax variables are low. It is also assumed

that the amount withheld is correct in the sense that it assumes that the exact amount withheld is

correct and that the employer withheld the exact correct amount: did not over-withhold or under-

withhold. Finally, all that is asked is how much was withheld in your last paycheck. This amount

is divided by gross pay last paycheck to estimate a tax rate. This estimated tax rate is applied to

total salary earnings in the twelve months. The constant tax rate assumption works well for

someone continuously employed and receiving about the same rate of pay over the past twelve

months. The assumption is less valid for other situations such as those that receive a positive or

negative wage shock. Overall even the reported values can only be considered rough

approximations to income taxes for the minority that actually report taxes.

Therefore we estimate taxes for all consumer units using the National Bureau of

Economic Research’s (NBER) TAXSIM program (see Feenberg and Coutts, 1993).45

The first step in estimating taxes is defining a tax filing unit. The unit of observation in

the CE Survey is a consumer unit. A consumer unit may have more than one tax filing unit

within it. Any person in the CU that was not the reference person or spouse of the reference

person that had earned income46

above the standard deduction for a single person would be her

own tax filing unit.47

Starting in 1985, there is a higher standard deduction for those 65 years or

older, and this value was used for those 65+. In 2011, the standard deduction was $5,800, and it

was $7,250 for individuals ages 65+.

Any person that was not his/her own tax filing unit was assumed to be a member of the

primary tax filing unit. There may be two adults in the consumer unit that were not the reference

person or spouse. We did not attempt to discern whether these two other adults might be married.

There is no way to guarantee that these two individuals are married. An aunt and uncle living in

the home could be married or could be brother and sister. Similarly we did not attempt to assign

any individual under the age of 19 who was not the child or adopted child of the reference person

as a dependent of a separate tax filing unit because it is impossible to know with certainty who

could claim this child as a dependent. There may be an adult child and a grandchild under the

age of 19 in the home but that the grandchild is not the child of the adult child. There is little or

no benefit in attempting to assign these individuals to a secondary tax filing unit.

With the filing units defined as above, the next step is to create the 22 input variables

allowed by the TAXSIM model. These are discussed in the order shown in the Internet interface

for TAXSIM.

1) ID is a variant of the consumer unit identification variable.

2) Tax year is defined off of the interview month and year. If the interview took place in

June or earlier, the tax year is the year before the interview year. If the interview took

place in July or later, the tax year is the year of the interview.

3) State is defined as state of residence. State taxes are not estimated after 2008 in

TAXSIM. To estimate states taxes after 2008, we use the 2008 tax rates for the given

45

http://www.nber.org/taxsim/ 46

Earned income is the sum of wage and salary income, non-farm self-employment income, and farm income. All

three variables are measured at the individual level in the CE Survey. 47

The values of the standard deduction were found here in February 2012

http://www.taxpolicycenter.org/taxfacts/displayafact.cfm?DocID=171&Topic2id=30&Topic3id=39.

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state. More detail is given below about the state because the CE Survey suppresses or re-

codes some states.

4) Marital status can be single, joint, head of household, or dependent taxpayer. For those

reference persons that are single with no children in the consumer unit, we assume the

person filed as single. We do not know if the person had a child living outside his

consumer unit for which he could claim as a dependent. We assume all married couples

file jointly. Any secondary tax filing unit in the consumer unit is treated as filing as

single.

5) A child is counted as a dependent exemption if the child is younger than 19 and is a

relative of the reference person. A child ages 19-24 years old is counted as a dependent if

the child is a relative and the child is in college full-time.

6) The number of taxpayers over age 65 references the ages of the reference person and

spouse only. TAXSIM requires this variable to be equal to 0, 1, or 2.

7) Wage and salary income of the taxpayer equals the earned income of the reference

person. Earned income is the sum of wage and salary income, non-farm self-employment

income, and farm income. We subtract off pension contributions made by the individual

out of his/her paycheck. These contributions are assumed to be tax deductible, and it is

assumed that the contributions are at or below the statutory maximum. Pension

contributions share one of the problems we had with reported taxes – the question

regarding pension contributions addresses the most recent paycheck.

8) Wage and salary income of the spouse equals the earned income of everyone in the

consumer unit except the reference person, if present. We also subtract off pension

contributions of these other CU members. The only reason TAXSIM creates a different

for the spouse is to calculate the marginal tax rate with respect to the taxpayer’s earnings

and with respect to the spouse’s earnings, which is important for the analysis of the effect

of taxes. We are only interested in total taxes paid, not the marginal tax rates.

9) The variable Dividends includes regular income from dividends, royalties, estates, and

trusts. These income sources cannot be separated in the CE Survey.

10) Other property income is the sum of interest income, net income or loss from roomers

and boarders, net income or loss from other rental units, alimony received, other money

income such as cash scholarships and fellowships and money received for being a foster

parent, and lump sum income such as income from estates, trusts, royalties, or games of

chance.

11) Taxable pensions equal the sum of pension and annuity income.

12) Gross social security benefits represent social security and railroad retirement income

before deductions for medical insurance and Medicare.

13) Other non-taxable transfer income is the sum of public assistance and welfare income,

regular child support payments received, lump sum child support payments received, and

food stamp/SNAP benefits.

14) Rent paid equals total rental payments excluding rent received as pay.

15) Real estate property taxes are the sum of all property taxes paid.

16) The components of other items are not available in the CE Survey, and the variable is set

to zero.

17) Child care expenses are the sum of all child care expenses.

18) Unemployment compensation represents all unemployment compensation income in the

last year.

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19) Number of dependents under age 17 is the count of people under age 17 in the

consumer unit.

20) Deductions not included elsewhere include mortgage payments, cash contributions, and

out-of-pocket health expenditures.

21) Short-term capital gains are not available in the CE Survey and are set to zero.

22) Long-term capital gains are not available in the CE Survey and are set to zero.

Variables 5, 6, 8, and 9-20 only get assigned to the reference person and spouse. All secondary

tax filing units are assigned a zero dollar value for these variables.

State identifiers

To protect the confidentiality of some respondents, the CE Survey suppresses some state

identifiers. For example, in the 2011 CE Survey any respondent living in Arkansas, Mississippi,

Montana, North Carolina, or South Dakota has a missing value for the state identifier. Other

states, such as Ohio, only have a portion of its respondents suppressed.

The CE Survey also re-codes some state identifiers. The state variable may be reported

but the respondent may be re-coded as living in another state. Someone living in Minnesota may

be re-coded as living in Wisconsin.

The suppression and re-coding of states is important because we estimate state income

taxes and because tax filers can deduct state income taxes on the federal income tax return.

States can have vastly different income tax rates.

The CE Survey documentation indicates what states have been suppressed and/or re-

coded, and it lists the states that are recipients of re-codes as well. We use this information along

with the region of residence (Northeast, Midwest, South, and West) to identify the potential

states a consumer unit lives in. For example in 2011 if region was equal to Northeast and state

was missing, the CE documentation indicates that only residents and Maine and New York were

suppressed. Thus we know that the consumer unit lived in either Maine or New York. For these

consumer units, we create two observations, one for the CU living in Maine and one for the CU

living in New York. Taxes are calculated using both states, and then the weighted average of

taxes is estimated using the state’s population in each year as the weight.

The suppression and re-coding patterns change with each sample redesign based on the

new Decennial Census of Population. The CE redesigns were in 1986, 1996, and 2005.

Finally from 1984-1995 and from 2006 on, the region variable could be missing. If state

is suppressed or re-coded and region is missing, then the possible states the CU lives in is the

population of all states that are re-coded or suppressed in the CE Survey in that year.

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Appendix D: Proof that Gini for maximum and minimum lie between consumption and

income Gini.

Notation:

y = {y1, ..,yn} the vector of income for the population of size n.

c = {c1, ..,cn} the vector of consumption for the population of size n.

Mi = max{yi,ci}the maximum of income and consumption for person i.

mi = min{yi,ci}the minimum of income and consumption for person i

M = {M1, ..,Mn}and m = {m1, ..,mn}.

I(c,y) the inequality of the vector of consumption and income, hence I(c,y) = I(c1, ..,cn,y1, ..,yn )

c, y,M,m, are the respective means for c, y, M and m.

i = 0.5*(yi+ ci) the average of income and consumption for person i.

Using decomposition techniques,

(1) I(c,y) = 0.5*I(c) + 0.5*I(y) + I(c, y) . By autonomy, I(c,y) = I(c1,y1 , …, cn,yn) and by decomposition

(2) I(c,y) = 1/ni

I )y,c( ii + I(1,…,n)

Combining (1) and (2), we have

(3) I(c) + I(y) = 2*(1/ni

I )y,c( ii + I(1,…,n) - I(c, y) )

For the max and min, by autonomy, I(c,y) = I(M1,m1 , …, Mn,mn).

Using similar techniques given in (1)-(3) yields

(4) I(M) + I(m) = I(c) + I(y) +2*( I(c, y) - I(M, m) )

Since ( I(c, y) - I(M, m) ) < 0, I(M) + I(m) < I(c) + I(y)

Note that M = {cz1,…,czj,yzj+1,…,yzn}={C1,Y2}, where czi yzi, for zi zj .

And m = {yz1,…,yzj,czj+1,…,czn}= {Y1,C2}.

Hence I(M) = I(C1,Y2) and using (1)

(5) I(M) = zi/n I(C1) + (1-zi)/n I(Y2) + I(c1, y2) Similarly,

(6) I(c) =(zi/n)I(C1) + ((1-zi)/n) I(C2) + I(c1, c2)

(7) I(y) = zi/n I(Y1) + (1-zi)/n I(Y2) + I(y1, y2)

(8) I(m) = zi/n I(Y1) + (1-zi)/n I(C2) + I(y1, c2) Using (7) and (8) and (5) yields

(5a) I(M) = I(y) + (zi/n) [I(C1) - I(Y1)] + [I(c1, y2) - I(y1, y2)] and

(5b) I(M) = I(c) – ((1-zi)/n) [I(C2) - I(Y2)] - [I(c1, c2) - I(c1, y2)] Alternatively, using (4) implies that

(9) I(M) = I(y) +2*( I(c, y) - I(M, m) ) +

zi/n( I(C1) – I(Y1)) +

I(c1, c2) - I(y1, c2) Claim: (10) I(c) < I(M) < I(y) if

(11) c2 > c1 and I(C2) < I(Y2)

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Idea of proof: The second term on the RHS of equation (10) is negative. By definition, c1 y1

and c2 y2 . If we assume that the distribution of y and c are such that it is more likely that c

> y for those on the lower end of the distribution, then c2 > c1 and the last term is negative.

And (11) guarantees that the third term is negative, i.e., that I(Ck) < I(Yk) for “most” groups k.

For example, if ci = a +byi (a0 and 0 < b < 1), then (11) holds. More generally, if ci = a +byi +

ei (a0 and 0 < b < 1), and there is no heteroskedasticity, that is e1 = e2 = 0 and e1 = e2 then

(11) holds.